Modified Gravity and Cosmology

THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

This article is devoted to the perturbative renormalization of the abelian Higgs-Kibble model, within the class of renormalizable gauges which are odd under charge conjugation. The Bogoliubov Parasiuk Hepp-Zimmermann renormalization scheme is used throughout, including the renormalized action principle proved by Lowenstein and Lam. The whole study is based on the fulfillment to all orders of perturbation theory of the Slavnov identities which express the invariance of the Lagrangian under a supergauge type family of non-linear transformations involving the Faddeev-Popov ghosts. Direct combinatorial proofs are given of the gauge independence and unitarity of the physicalS operator. Their simplicity relies both on a systematic use of the Slavnov identities as well as suitable normalization conditions which allow to perform all mass renormalizations, including those pertaining to the ghosts, so that the theory can be given a setting within a fixed Fock space. Some simple gauge independent local operators are constructed.

/pdf/renormalization-of-the-abelian-higgs-kibble-model-14fr0vp7oj.pdf

Renormalization of the Abelian Higgs-Kibble Model

A Call for New Physics : The Muon Anomalous Magnetic Moment and Lepton Flavor Violation

Proton stability in grand unified theories, in strings and in branes

In 1938, Stueckelberg introduced a scalar field which makes an Abelian gauge theory massive but preserves gauge invariance. The Stueckelberg mechanism is the introduction of new fields to reveal a symmetry of a gauge--fixed theory. We first review the Stueckelberg mechanism in the massive Abelian gauge theory. We then extend this idea to the standard model, stueckelberging the hypercharge U(1) and thus giving a mass to the physical photon. This introduces an infrared regulator for the photon in the standard electroweak theory, along with a modification of the weak mixing angle accompanied by a plethora of new effects. Notably, neutrinos couple to the photon and charged leptons have also a pseudo-vector coupling. Finally, we review the historical influence of Stueckelberg's 1938 idea, which led to applications in many areas not anticipated by the author, such as strings. We describe the numerous proposals to generalize the Stueckelberg trick to the non-Abelian case with the aim to find alternatives to the standard model. Nevertheless, the Higgs mechanism in spontaneous symmetry breaking remains the only presently known way to give masses to non-Abelian vector fields in a renormalizable and unitary theory.

The Stueckelberg Field

New R-matrices associated with finite dimensional representations of Uq(sl(2)) at roots of unity

The contour picture of quantum groups: Conformal field theories

Explicit quantum symmetries of WZNW theories

https://archive-ouverte.unige.ch/unige:115694/ATTACHMENT01

M. Ruiz-Altaba

Papers

The Stueckelberg Field

New R-matrices associated with finite dimensional representations of Uq(sl(2)) at roots of unity

The contour picture of quantum groups: Conformal field theories

Explicit quantum symmetries of WZNW theories

New solutions to the Yang-Baxter equation from two-dimensional representations of Uq(sl(2)) at roots of unity